Spacetime Virasoro algebra from strings on zero radius AdS₃

الأصل · EN

We study bosonic string theory in the light-cone gauge on AdS₃ spacetime with zero radius of curvature (in string units) R/√α′=0. We find that the worldsheet theory admits an infinite number of conserved quantities which are naturally interpreted as spacetime charges and which form a representation of (two commuting copies of) a Virasoro algebra. Near the boundary of AdS₃ these charges are found to be isomorphic to the infinite set of asymptotic Killing vectors of AdS₃ found originally by Brown and Henneaux. In addition to the spacetime Virasoro algebra, there is a worldsheet Virasoro algebra that generates diffeomorphisms of the spatial coordinate of the string worldsheet. We find that if the worldsheet Virasoro algebra has a central extension then the spacetime Virasoro algebra acquires a central extension via a mechanism similar to that encountered in the context of the SL(2,R) WZW model.Our observations are consistent with a recently proposed duality between bosonic strings on zero radius AdSd+1 and free field theory in d dimensions.